import numpy as np
import pandas as pd
from itertools import cycle
from scipy import interp

# sklearn
from sklearn import metrics
from sklearn.model_selection import train_test_split, StratifiedShuffleSplit
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn import preprocessing

# TensorFlow
import tensorflow as tf

# Timer
from timeit import default_timer as timer

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## seaborn
import seaborn as sns

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
from matplotlib.font_manager import FontProperties
import matplotlib.colors as mcolors
from matplotlib import cm
plt.style.use('seaborn-whitegrid')
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

import warnings
warnings.filterwarnings("ignore")

Home / Healthcare Analytics and Modeling

Heart Disease Dataset

• Exploratory Data Analysis
• Modeling: Tensorflow Linear Classifier
• Modeling: Tensorflow DNN Classifier
• Modeling: Tensorflow Boosted Trees Classifier
• Modeling: Tensorflow Boosted Trees Classifier with Feature Importance Analysis

Heart Disease Dataset

In this article, we demonstrate solving a classification problem in TensorFlow using Estimators using the Heart Disease Dataset from the UCI Machine Learning Repository.

Picture Source: harvard.edu

Attribute Information:

1. Age
2. Sex
   • 0: Female
   • 1: Male
3. Chest Pain Type
   • 1: Typical Angina
   • 2: Atypical Angina
   • 3: Non-Anginal Pain
   • 4: Asymptomatic

• Resting Blood Pressure

1. Serum Cholestoral (in mg/dl )
2. FBS: Fasting Blood Sugar > 120 mg/dl
   • 0 = False
   • 1 = True
3. Resting Electrocardiographic Results
   • 0: normal
   • 1: having ST-T wave abnormality (T wave inversions and/or ST elevation or depression of > 0.05 mV)
   • 2: showing probable or definite left ventricular hypertrophy by Estes' criteria
4. Maximum Heart Rate Achieved
5. Exercise Induced Angina
   • 0: No
   • 1: Yes
6. Oldpeak = St Depression Induced By Exercise Relative To Rest
7. Slope: The Slope Of The Peak Exercise ST Segment
   • 1: Upsloping
   • 2: Flat
   • 3: Downsloping
8. Number Of Major Vessels (0-3) Colored By Flourosopy
9. Thal
   • 3: Normal
   • 6: Fixed Defect
   • 7: Reversable Defect

Variable to be predicted

• Heart Disease
  • 0: Absence
  • 1: Presence

Problem Description

The object of the exercise is to develop a predictive model that can predict whether heart disease is present or absent based on the rest of the given features.

Data = np.genfromtxt('heart-disease/heart.dat', delimiter=' ')
Attributes = ['Age', 'Sex', 'Chest Pain Type', 'Resting Blood Pressure', 'Serum Cholestoral',
              'Fasting Blood Sugar', 'Resting Electrocardiographic Results', 'Maximum Heart Rate Achieved',
              'Exercise Induced Angina', 'Oldpeak', 'Slope',
              'Number of Major Vessels', 'Thal', 'Heart Disease']
Data = pd.DataFrame(data = Data, columns = Attributes)
# 
Temp = ['Sex', 'Chest Pain Type', 'Fasting Blood Sugar', 'Resting Electrocardiographic Results',
       'Exercise Induced Angina', 'Slope', 'Number of Major Vessels','Thal']
for c in Temp:
    Data[c] = Data[c].astype(int).astype(str)
del Temp, c
Target = 'Heart Disease'
Labels_dict = dict(zip([0,1],['Absent', 'Present']))
Data['Heart Disease'] = (Data['Heart Disease']-1).astype(int)
#
display(Data.head(5))
display(pd.DataFrame({'Number of Instances': [Data.shape[0]], 'Number of Attributes': [Data.shape[1]]}).style.hide_index())

# Maps
Maps = {'Sex': {'0':'Female', '1':'Male'},
        'Chest Pain Type': {'1':'Typical Angina', '2':'Atypical Angina', '3': 'Non-Anginal Pain', '4':'Asymptomatic'},
        'Fasting Blood Sugar': {'0': 'False', '1': 'True'}, 'Exercise Induced Angina': {'0': 'No', '1': 'Yes'},
        'Slope': {'1': 'Upsloping', '2': 'Flat', '3': 'Downsloping'},
        'Thal':  {'3': 'Normal', '6': 'Fixed Defect','7': 'Reversable Defect'}}

	Age	Sex	Chest Pain Type	Resting Blood Pressure	Serum Cholestoral	Fasting Blood Sugar	Resting Electrocardiographic Results	Maximum Heart Rate Achieved	Exercise Induced Angina	Oldpeak	Slope	Number of Major Vessels	Thal	Heart Disease
0	70.0	1	4	130.0	322.0	0	2	109.0	0	2.4	2	3	3	1
1	67.0	0	3	115.0	564.0	0	2	160.0	0	1.6	2	0	7	0
2	57.0	1	2	124.0	261.0	0	0	141.0	0	0.3	1	0	7	1
3	64.0	1	4	128.0	263.0	0	0	105.0	1	0.2	2	1	7	0
4	74.0	0	2	120.0	269.0	0	2	121.0	1	0.2	1	1	3	0

Number of Instances	Number of Attributes
270	14

def Data_Plot(Inp, Title = None, W = None):
    data_info = Inp.dtypes.astype(str).to_frame(name='Data Type')
    Temp = Inp.isnull().sum().to_frame(name = 'Number of NaN Values')
    data_info = data_info.join(Temp, how='outer')
    data_info ['Size'] = Inp.shape[0]
    data_info['Percentage'] = 100 - np.round(100*(data_info['Number of NaN Values']/Inp.shape[0]),2)
    data_info = data_info.reset_index(drop = False).rename(columns = {'index':'Features'})
    #
    fig = px.bar(data_info, x= 'Features', y= 'Percentage', color = 'Data Type',
                 text = 'Percentage',
                 color_discrete_sequence = ['PaleGreen', 'LightCyan', 'PeachPuff', 'Pink', 'Plum'],
                 hover_data = data_info.columns)
    fig.update_layout(plot_bgcolor= 'white', legend=dict(x=1.01, y=.5, traceorder="normal",
                                                         bordercolor="DarkGray", borderwidth=1))
    if not W == None:
        fig.update_layout(width = W)
    fig.update_traces(texttemplate= 10*' ' + '%%{text}', textposition='inside')
    fig.update_traces(marker_line_color= 'Black', marker_line_width=1., opacity=1)
    if not Title == None:
        fig.update_layout(title={'text': '<b>' + Title + '<b>', 'x':0.5,
                                         'y':0.90, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()
    return data_info

data_info = Data_Plot(Data, Title = 'Heart Disease Dataset', W = 800)

X and y sets

# A copy of the Dataframe
df = Data.copy()
# for TF
df.columns = [x.replace(' ','_') for x in df.columns] 
Temp = Target.replace(' ','_')
X = df.drop(columns = Temp)
y = df[Temp].values
del df, Temp

Training and testing sets

def DatasetTargetDist(Inp, Target, Labels_dict, PD):
    # Table
    Table = Inp[Target].value_counts().to_frame('Count').reset_index(drop = False).rename(columns = {'index':Target})
    Table[Target] = Table[Target].replace(Labels_dict)
    Table['Percentage'] = np.round(100*(Table['Count']/Table['Count'].sum()),2)
    fig = make_subplots(rows=1, cols=2, horizontal_spacing = 0.02, column_widths=PD['column_widths'],
                        specs=[[{"type": "table"},{"type": "pie"}]])

    # Right
    fig.add_trace(go.Pie(labels=Table[Target].values, values=Table['Count'].values,
                         pull=PD['pull'], textfont=dict(size= PD['textfont']),
                         marker=dict(colors = PD['PieColors'], line=dict(color='black', width=1))), row=1, col=2)
    fig.update_traces(hole=PD['hole'])
    fig.update_layout(height = PD['height'], legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
    
    # Left
    T = Table.copy()
    T['Percentage'] = T['Percentage'].map(lambda x: '%%%.2f' % x)
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)

    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= PD['TableColors'][0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [PD['TableColors'][1], PD['TableColors'][1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)

    fig.update_layout(title={'text': '<b>' + Target + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

Pull = [0 for x in range((len(Labels_dict)-1))]
Pull.append(.05)
PD = dict(PieColors = ['SeaGreen','FireBrick'],
          TableColors = ['Navy','White'], hole = .4,
          column_widths=[0.6, 0.4],textfont = 14, height = 350, tablecolumnwidth = [0.20, 0.12, 0.15],
          pull = Pull, legend_title = Target, title_x = 0.5, title_y = 0.8)
del Pull
DatasetTargetDist(Data, Target, Labels_dict, PD)

StratifiedKFold is a variation of k-fold which returns stratified folds: each set contains approximately the same percentage of samples of each target class as the complete set.

Test_Size = 0.3
sss = StratifiedShuffleSplit(n_splits=1, test_size=Test_Size, random_state=42)
_ = sss.get_n_splits(X, y)
# For Tensorflow
X.columns = [x.replace(' ','_') for x in X.columns]

for train_index, test_index in sss.split(X, y):
    # X
    if isinstance(X, pd.DataFrame):
        X_train, X_test = X.loc[train_index], X.loc[test_index]
    else:
        X_train, X_test = X[train_index], X[test_index]
    # y    
    if isinstance(y, pd.Series):
        y_train, y_test = y[train_index], y[test_index]
    else:
        y_train, y_test = y[train_index], y[test_index]
del sss

def Train_Test_Dist(X_train, y_train, X_test, y_test, PD, Labels_dict = Labels_dict):
    def ToSeries(x):
        if not isinstance(x, pd.Series):
            Out = pd.Series(x)
        else:
            Out = x.copy()
        return Out
    
    fig = make_subplots(rows=1, cols=3, horizontal_spacing = 0.02, column_widths= PD['column_widths'],
                        specs=[[{"type": "table"},{'type':'domain'}, {'type':'domain'}]])
    # Right
    C = 2
    for y in [ToSeries(y_train).replace(Labels_dict), ToSeries(y_test).replace(Labels_dict)]:
        fig.add_trace(go.Pie(labels= list(Labels_dict.values()),
                             values= y.value_counts().values, pull=PD['pull'],
                             textfont=dict(size=PD['textfont']),
                             marker=dict(colors = PD['PieColors'],
                             line=dict(color='black', width=1))), row=1, col=C)
        fig.update_traces(hole=.5)
        fig.update_layout(legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
        C+=1
    
    # Left
    
    # Table
    Table = pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
                       'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).astype(str)
    T = Table.copy()
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)
        
    TableColors = PD['TableColors']
    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= TableColors[0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [TableColors[1], TableColors[1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)
    fig.update_layout(title={'text': '<b>' + 'Dataset Distribution' + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    if not PD['height'] == None:
        fig.update_layout(height = PD['height'])
    fig.show()
    
PD.update(dict(column_widths=[0.3, 0.3, 0.3], tablecolumnwidth = [0.2, 0.4], height = 350, legend_title = Target))

Train_Test_Dist(X_train, y_train, X_test, y_test, PD)

Modeling: Tensorflow Linear Classifier

Here, we use the Tensorflow Linear classifier model.tf.estimator.LinearClassifier.

Input Function

The input function specifies how data is converted to a tf.data.Dataset that feeds the input pipeline in a streaming fashion. Moreover, an input function is a function that returns a tf.data.Dataset object which outputs the following two-element tuple:

• features - A Python dictionary in which:
  • Each key is the name of a feature.
  • Each value is an array containing all of that feature's values.
• label - An array containing the values of the label for every example.

def input_fn(features, labels, training=True, batch_size=256):
    """An input function for training or evaluating"""
    # Convert the inputs to a Dataset.
    dataset = tf.data.Dataset.from_tensor_slices((dict(features), labels))

    # Shuffle and repeat if you are in training mode.
    if training:
        dataset = dataset.shuffle(1000).repeat()
    
    return dataset.batch(batch_size)

Moreover, an estimator model consists of two main parts, feature columns, and a numeric vector. Feature columns provide explanations for the input numeric vector. The following function separates categorical and numerical columns (features)and returns a descriptive list of feature columns.

def Feat_Columns(Inp):
    Temp = Inp.dtypes.reset_index(drop = False)
    Temp.columns = ['Features', 'Data Type']
    Temp['Data Type'] = Temp['Data Type'].astype(str)
    # Numeric_Columns
    Numeric_Columns = Temp.loc[Temp['Data Type'].isin(['int64', 'int32', 'float64', 'float32']),'Features'].tolist()
    # Categorical_Columns
    Categorical_Columns = Temp.loc[Temp['Data Type'] == 'object','Features'].tolist()
        
    # Feature Columns
    feature_columns = []
    if len(Categorical_Columns)>0:
        for feature_name in Categorical_Columns:
          vocabulary = Inp[feature_name].unique()
          feature_columns.append(tf.feature_column.categorical_column_with_vocabulary_list(feature_name, vocabulary))
    if len(Numeric_Columns)>0:
        for feature_name in Numeric_Columns:
          feature_columns.append(tf.feature_column.numeric_column(feature_name))
    return feature_columns

my_feature_columns = Feat_Columns(X)

Estimator using the Default Optimizer

tf.keras.backend.clear_session()
IT = int(5e3)
classifier = tf.estimator.LinearClassifier(feature_columns=my_feature_columns)
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8765	0.5556	0.9148	0.846	0.4334	0.4444	0.4334	0.825	0.5008	0.9167	5000

ROC Curves

def ROC_Curve(y_test, probs, n_classes, FS = 7, ax = False, pad = 0.01):
    # converting y_test to categorical
    y_test_cat = tf.keras.utils.to_categorical(y_test, num_classes=n_classes, dtype='float32')
    # Compute ROC curve and ROC area for each class
    fpr = dict()
    tpr = dict()
    roc_auc = dict()
    for i in range(n_classes):
        fpr[i], tpr[i], _ = metrics.roc_curve(y_test_cat[:, i], probs[:, i])
        roc_auc[i] = metrics.auc(fpr[i], tpr[i])

    # Compute micro-average ROC curve and ROC area
    fpr["micro"], tpr["micro"], _ = metrics.roc_curve(y_test_cat.ravel(), probs.ravel())
    roc_auc["micro"] = metrics.auc(fpr["micro"], tpr["micro"])

    # First aggregate all false positive rates
    all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))

    # Then interpolate all ROC curves at this points
    mean_tpr = np.zeros_like(all_fpr)
    for i in range(n_classes):
        mean_tpr += interp(all_fpr, fpr[i], tpr[i])

    # Finally average it and compute AUC
    mean_tpr /= n_classes

    fpr["macro"] = all_fpr
    tpr["macro"] = mean_tpr
    roc_auc["macro"] = metrics.auc(fpr["macro"], tpr["macro"])

    fig = go.Figure()
    fig.add_trace(go.Scatter(x=[0, 1], y=[0, 1], name = 'FPR = TPR', line = dict(color='Black', width=2, dash='dash')))
    fig.add_trace(go.Scatter(x=fpr["micro"], y=tpr["micro"], mode='lines', marker_color = 'deeppink',
                             name='micro-average ROC curve (area = {0:0.2f})'.format(roc_auc["micro"])))
    fig.add_trace(go.Scatter(x=fpr["macro"], y=tpr["macro"], mode='lines', marker_color = 'navy',
                             name='macro-average ROC curve (area = {0:0.2f})'.format(roc_auc["macro"])))

    colors = cycle(['Aqua', 'DarkOrange', 'CornflowerBlue'])
    for i, color in zip(range(n_classes), colors):
        _ = fig.add_trace(go.Scatter(x = fpr[i], y = tpr[i], mode='lines', marker_color= px.colors.sequential.Rainbow,
                                     name='ROC curve of class {0} (area = {1:0.2f})'.format(i, roc_auc[i])))

    # Background
    fig.update_layout(plot_bgcolor= 'white')
    fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'False Positive Rate (FPR)')
    fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'True Positive Rate (TPR)')
    fig.update_yaxes(scaleanchor = "x", scaleratio = 1)
    fig.update_layout(height = 600, width = 810)
    fig.update_layout(title={'text': '<b>' + 'Receiver Operating Characteristic (ROC) Curves' + '<b>', 'x': .5,
                                         'y': .9, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm. Note that due to the size of data, here we don't provide a Cross-validation evaluation. In general, this type of evaluation is preferred.

def Confusion_Mat(CM_Train, CM_Test, PD, n_splits = 10):
    if n_splits == None:
        Titles = ['Train Set', 'Test Set']
    else:
        Titles = ['Train Set (CV = % i)' % n_splits, 'Test Set (CV = % i)' % n_splits]
    CM = [CM_Train, CM_Test]
    Cmap = ['Greens', 'YlGn','Blues', 'PuBu']
    for i in range(2):
        fig, ax = plt.subplots(1, 2, figsize= PD['FS'])
        fig.suptitle(Titles[i], weight = 'bold', fontsize = 16)
        _ = sns.heatmap(CM[i], annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i], ax = ax[0],
                        linewidths = 0.2, cbar_kws={"shrink": PD['shrink']})
        _ = ax[0].set_title('Confusion Matrix');
        Temp = np.round(CM[i].astype('float') / CM[i].sum(axis=1)[:, np.newaxis], 2)
        _ = sns.heatmap(Temp,
                        annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i+1], ax = ax[1],
                       linewidths = 0.4, vmin=0, vmax=1, cbar_kws={"shrink": PD['shrink']})
        _ = ax[1].set_title('Normalized Confusion Matrix');

        for a in ax:
            _ = a.set_xlabel('Predicted labels')
            _ = a.set_ylabel('True labels'); 
            _ = a.xaxis.set_ticklabels(PD['Labels'])
            _ = a.yaxis.set_ticklabels(PD['Labels'])
            _ = a.set_aspect(1)

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (10, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	0.858407	0.923810	0.889908	105.000000
Present	0.894737	0.809524	0.850000	84.000000
accuracy	0.873016	0.873016	0.873016	0.873016
macro avg	0.876572	0.866667	0.869954	189.000000
weighted avg	0.874554	0.873016	0.872171	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.926829	0.844444	0.883721	45.000000
Present	0.825000	0.916667	0.868421	36.000000
accuracy	0.876543	0.876543	0.876543	0.876543
macro avg	0.875915	0.880556	0.876071	81.000000
weighted avg	0.881572	0.876543	0.876921	81.000000

Estimator using the FTRL Optimizer with Regularization

The Follow the Regularized Leader (FTRL) model is an implementation of the FTRL-Proximal online learning algorithm for binomial logistic regression (for details see [6]).

tf.keras.backend.clear_session()
IT = int(5e3)
classifier = tf.estimator.LinearClassifier(feature_columns=my_feature_columns,
                          optimizer=tf.keras.optimizers.Ftrl(learning_rate=0.1, l1_regularization_strength=0.001))
#
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8765	0.5556	0.9247	0.8833	0.4117	0.4444	0.4117	0.8095	0.528	0.9444	5000

ROC Curves

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (10, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	0.878505	0.895238	0.886792	105.000000
Present	0.865854	0.845238	0.855422	84.000000
accuracy	0.873016	0.873016	0.873016	0.873016
macro avg	0.872179	0.870238	0.871107	189.000000
weighted avg	0.872882	0.873016	0.872850	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.948718	0.822222	0.880952	45.000000
Present	0.809524	0.944444	0.871795	36.000000
accuracy	0.876543	0.876543	0.876543	0.876543
macro avg	0.879121	0.883333	0.876374	81.000000
weighted avg	0.886854	0.876543	0.876882	81.000000

Estimator using an Optimizer with a Learning Rate Decay

tf.keras.backend.clear_session()
IT = int(5e3)
classifier = tf.estimator.LinearClassifier(feature_columns=my_feature_columns,
            optimizer=lambda: tf.keras.optimizers.Adam(learning_rate=tf.compat.v1.train.exponential_decay(learning_rate=0.1,
            global_step=tf.compat.v1.train.get_global_step(), decay_steps=IT,decay_rate=0.96)))
#
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8148	0.5556	0.8843	0.7893	0.9979	0.4444	0.9979	0.7234	0.595	0.9444	5000

ROC Curves

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (10, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	0.912088	0.790476	0.846939	105.000000
Present	0.775510	0.904762	0.835165	84.000000
accuracy	0.841270	0.841270	0.841270	0.841270
macro avg	0.843799	0.847619	0.841052	189.000000
weighted avg	0.851387	0.841270	0.841706	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.941176	0.711111	0.810127	45.000000
Present	0.723404	0.944444	0.819277	36.000000
accuracy	0.814815	0.814815	0.814815	0.814815
macro avg	0.832290	0.827778	0.814702	81.000000
weighted avg	0.844389	0.814815	0.814193	81.000000

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References

1. Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M., Schmid, J.J., Sandhu, S., Guppy, K.H., Lee, S. and Froelicher, V., 1989. International application of a new probability algorithm for the diagnosis of coronary artery disease. The American journal of cardiology, 64(5), pp.304-310.
2. Aha, D. and Kibler, D., 1988. Instance-based prediction of heart-disease presence with the Cleveland database. University of California, 3(1), pp.3-2.
3. Gennari, J.H., Langley, P. and Fisher, D., 1989. Models of incremental concept formation. Artificial intelligence, 40(1-3), pp.11-61.
4. Regression analysis Wikipedia page
5. Tensorflow tutorials
6. TensorFlow Boosted Trees Classifier
7. Lasso (statistics) Wikipedia page)
8. Tikhonov regularizationm Wikipedia page
9. Palczewska A., Palczewski J., Marchese Robinson R., Neagu D. (2014) Interpreting Random Forest Classification Models Using a Feature Contribution Method. In: Bouabana-Tebibel T., Rubin S. (eds) Integration of Reusable Systems. Advances in Intelligent Systems and Computing, vol 263. Springer, Cham
10. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 112, pp. 3-7). New York: springer.
11. Jordi Warmenhoven, ISLR-python
12. James, G., Witten, D., Hastie, T., & Tibshirani, R. (2017). ISLR: Data for an Introduction to Statistical Learning with Applications in R

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